Extremely High Energy Neutrinos, Neutrino Hot Dark Matter, and the Highest Energy Cosmic Rays

Extremely high energy ( $\sim {10}^{22}\mathrm{eV}$) cosmic neutrino beams initiate high energy particle cascades in the background of relic neutrinos from the big bang. We perform numerical calculations to show that such cascades could contribute more than 10% to the observed cosmic ray flux above $3\times {10}^{19}\mathrm{eV}$ if neutrinos have $\sim \mathrm{eV}$ masses. The required intensity of primary neutrinos could be consistent with astrophysical models for their production if the maximum neutrino energy reaches to $\sim {10}^{22}\mathrm{eV}$ and the massive neutrino dark matter is locally clustered. Future observations of ultrahigh energy cosmic rays will lead to an indirect but practical search for neutrino dark matter.